Aggregation and the Microfoundations of Dynamic Macroeconomics

This book argues that modern macroeconomics has completely overlooked the aggregate nature of the data. Standard models start with intertemporally maximizing agents and obtain dynamic equations linking economic variables like consumption, income, investment interest rate and employment. Such equations exhibit testable properties like cointegration, definite patterns of Granger causality, and restrictions on the parameters. The usual simplification that agents are identical leads to testing these properties directly on aggregate data. Here this simplification is systematically questioned. In Part I the homogeneity assumption is tested using disaggregate data and strongly rejected. As shown in Part II, the consequence of introducing heterogeneity is that, apart from flukes, cointegration unidirectional Granger causality, restrictions on parameters do not survive aggregation: thus the claim that modern macroeconomics has solid microfoundations is unwarranted. However, it is argued in Part III that aggregation is not necessarily bad. Some important theory-based models that do not fit aggregate data well in their representative-agent version can be reconciled with aggregate data by introducing heterogeneity.

Table of Contents:
INTRODUCTION ; LIST OF SYMBOLS ; I. AGGREGATION OF SCALAR PROCESSES ; 1. COMMON AND IDIOSYNCRATIC COMPONENTS ; 1.1. THE MODEL FOR THE INDIVIDUAL VARIABLES ; 1.2. A LARGE NUMBER OF AGENTS ; 1.3. LARGE NUMBERS: A GENERAL RESULT ; 1.4. A CONTINUUM OF AGENTS ; 1.5. AUTOREGRESSIVE RELATIONSHIPS AMONG THE MICROVARIABLES ; 1.6. BIBLIOGRAPHIC NOTES ; 2. HOW MANY COMMON SHOCKS? ; 2.1. PERFECT CORRELATION ; 2.2. PAIRWISE SINGULARITY ; 2.3. PAIRWISE COINTEGRATION ; 2.4. HOW MANY COMMON SHOCKS? ; 2.5. DYNAMIC PRINCIPAL COMPONENTS ; 2.6. FURTHER EMPIRICAL EVIDENCE ; 2.7. BIBLIOGRAPHIC NOTES ; 3. THE REGIONAL MODEL ; 3.1. FROM THE INDIVIDUAL TO THE REGIONAL MODEL ; 3.2. SPECIFICATION OF THE REGIONAL MODEL ; 3.3. ESTIMATION AND DIAGNOSTIC CHECKING ; 3.4. IDENTIFICATION OF THE COMMON SHOCKS ; 3.5. BIBLIOGRAPHIC NOTES ; 4. AGGREGATING THE COMMON COMPONENTS ; 4.1. THE WOLD REPRESENTATION OF THE MACROVARIABLE ; 4.2. IDENTIFICATION OF THE MICROPARAMETERS ; 4.3. BIBLIOGRAPHIC NOTES ; II. AGGREGATION OF ECONOMIC MODELS ; 5. REFORMULATION OF STANDARD REPRESENTATIVE-AGENT MODELS ; 5.1. LIFE CYCLE, PERMANENT INCOME UNDER RATIONAL EXPECTATIONS ; 5.2. A LABOR DEMAND SCHEDULE UNDER RATIONAL EXPECTATIONS ; 5.3. CONSUMPTION AND INCOME AGAIN: ERROR CORRECTION MECHANISMS ; 5.4. RULES OF THUMB. NON-FULLY RATIONAL, ROUTINIZED BEHAVIORS ; 5.5. STRUCTURAL VAR MODELS. GENERAL EQUILIBRIUM ; 5.6. BIBLIOGRAPHIC NOTES ; 6. THE DISAGGREGATED MODEL ; 6.1. THE MICROPARAMETER SPACE ; 6.2. THE MICROMODEL ; 6.3. THE POPULATION SPACE ; 6.4. THE DISAGGREGATED MODEL ; 6.5. FURTHER COMMENTS ON THE MICROMODEL. ANALYTIC FUNCTIONS ; 6.6. NEGLIGIBLE SUBSETS. THE ALTERNATIVE PRINCIPLE ; 6.7. NON-REDUNDANCY OF THE COMMON SHOCKS ; 6.8. DEPENDENT AND INDEPENDENT VARIABLES ; 6.9. THE MICROMODEL COEFFICIENTS AS ANALYTIC FUNCTIONS ; 6.10. BIBLIOGRAPHIC NOTES ; 7. THE AGGREGATE MODEL ; 7.1. DEFINITION OF THE AGGREGATE MODEL ; 7.2. DROPPING THE IDIOSYNCRATIC COMPONENT ; 7.3. AGGREGATION OF THE DI MODEL ; 7.4. MACROVARIABLES IN THE MICROMODEL. GENERAL EQUILIBRIUM ; 7.5. POPULATIONS AND DISTRIBUTIONS OVER [TYPE IN SYMBOL] ; 7.6. RESTRICTIONS AND SUBSETS OF THE POPULATION SPACE ; 7.7. BIBLIOGRAPHIC NOTES ; 8. THE RANK OF THE AGGREGATE VECTOR ; 8.1. GENERAL STATEMENTS ; 8.2. THE TWO-POINT EXAMPLE ; 8.3. A THEOREM FOR THE DI MODEL ; 8.4. MORE ON THE SUBSET OF [TYPE IN SYMBOL] WHERE THE MODEL IS SINGULAR ; 8.5. BIBLIOGRAPHIC NOTES ; 9. COINTEGRATION ; 9.1. GENERAL RESULTS ; 9.2. LOG-LINEAR MODELS ; 9.3. AN OBSERVATION ON THE ALTERNATIVE PRINCIPLE ; 9.4. BIBLIOGRAPHIC NOTES ; 10. AN EXTENSION OF THE ALTERNATIVE PRINCIPLE ; 10.1. FROM THE SPECTRAL DENSITY TO THE WOLD REPRESENTATION ; 10.2. AN EXTENSION OF THE ALTERNATIVE PRINCIPLE ; 10.3. BIBLIOGRAPHIC NOTES ; 11. GRANGER CAUSALITY ; 11.1. GENERAL RESULTS ; 11.2. DISCUSSION OF THE TWO-POINT EXAMPLE ; 11.3. BIBLIOGRAPHIC NOTES ; 12. WOLD REPRESENTATION: VAR AND ARMAX MODELS ; 12.1. VAR MODELS ; 12.2. FUNDAMENTALNESS ; 12.3. ARMAX MODELS ; 12.4. INTERPRETATION. OVERIDENTIFYING RESTRICTIONS ; 12.5. BIBLIOGRAPHIC NOTES ; III. MACROECONOMIC APPLICATIONS ; 13. PERMANENT INCOME AND THE ERROR CORRECTION MECHANISM ; 13.1. EXCESS SENSITIVITY ; 13.2. COINTEGRATION OF CONSUMPTION AND TOTAL INCOME ; 13.3. SINGULARITY ; 13.4. CONSUMPTION VOLATILITY ; 13.5. COMPLETE INFORMATION AND THE REPRESENTATIVE AGENT ; 13.6. AN EXPLANATION FOR SENSITIVITY AND SMOOTHNESS ; 13.7. MICRO AND MACRO SINGULARITY ; 13.8. RECONCILING PIH AND ECM ; 13.9. AN EMPIRICAL EXERCISE ; 13.10. BIBLIOGRAPHIC NOTES ; 14. DISAGGREGATING THE BUSINESS CYCLE ; 14.1. THE NUMBER OF COMMON SHOCKS ; 14.2. IDENTIFICATION OF THE COMMON TECHNOLOGY SHOCK ; 14.3. ESTIMATION OF THE SECTORAL MODEL ; 14.4. DIAGNOSTIC CHECKING, DATA SOURCES, AND DATA TREATMENT ; 14.5. SUMMARY ; CONCLUSIONS ; APPENDIX. ELEMENTS OF DISCRETE TIME SERIES THEORY ; A.1. ORTHOGONAL PROJECTIONS ; A.2. THE WOLD REPRESENTATION ; A.3. MA REPRESENTATIONS OF REGULAR PROCESSES ; A.4. NON-FUNDAMENTALNESS AND PREDICTION ; A.5. SCALAR ARMA PROCESSES ; A.6. VECTOR PROCESSES ; A.7. THE SPECTRAL DENSITY ; A.8. GRANGER CAUSALITY AND SIMS'S THEOREM ; A.9. BIBLIOGRAPHIC NOTES ; REFERENCES ; INDEX